<h2>Problem 169</h2>
<div style="color:#666;font-size:80%;">23 November 2007</div><br />
<div class="problem_content">
<p>Define f(0)=1 and f(<var>n</var>) to be the number of different ways <var>n</var> can be expressed as a sum of integer powers of 2 using each power no more than twice.</p>
<p>For example, f(10)=5 since there are five different ways to express 10:</p>
<p style="margin-left:50px;">1 + 1 + 8<br />
1 + 1 + 4 + 4<br />1 + 1 + 2 + 2 + 4<br />
2 + 4 + 4<br />
2 + 8</p>
<p>What is f(10<img src="" style="display:none;" alt="^(" /><sup>25</sup><img src="" style="display:none;" alt=")" />)?</p>

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